Teacher2Teacher 
Q&A #6524 
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From: Neil Sklar <rp_mcmurphy@hotmail.com> To: Teacher2Teacher Public Discussion Date: 2008071022:06:07 Subject: partial products Hi, Put simply, the reason the zeros need to be inserted is to cause the place values to line up correctly. I teach this by physically decomposing one of the factors into partial products, then adding the products together, as follows: 123 X 123 is equivalent to (120 X 100) + (120 X 20) + (120 X 3). 120 X 3 = 360 120 X 20 = (120 X 2 X 10) = 2400 120 X 2 = 240, and we can use the "trick" (though I prefer that students understand the reasoning behind it) of inserting a 0 at the end of the 240 to get 2400. 120 X 100 = (120 X 1 X 100) = 36000 120 X 1 = 120, and insert the two zeros to get 12000. Then add 360 + 2400 + 360000. If you do this to build understanding of concept before (or instead of) teaching the 'standard algorithm,' students are far more likely to understand that they need to insert the zeros so that the place values will be aligned correctly. Feel free to post or email me if you'd like more detail on how to present this. Good luck, Neil
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